Origins of Dielectric Loss in Materials for Superconducting Qubits

The coherence times of state-of-the-art superconducting qubits are limited by bulk dielectric loss, yet the microscopic processes leading to this loss are unclear. We present mechanisms that can plausibly explain the experimentally observed loss. Even high-purity materials contain unintentional impurities and/or point defects in concentrations of up to 10¹⁸ cm^-3. If these impurities or defects are charged (which they usually are) they can absorb electromagnetic radiation at GHz frequencies by emission of acoustic phonons [1]. Our derivation of the absorption coefficient for this mechanism leads to a loss tangent on the order of 10^-8 for Al₂O₃, a widely used substrate material, in good agreement with recent high-precision measurements [Phys. Rev. Appl. 19, 034064 (2023)]. Our study shows that the loss per defect depends mainly on properties of the host material, and a high-throughput search suggests that diamond, cubic BN, AlN, and SiC are optimal in this respect.

For paramagnetic impurities or defects, we propose an additional mechanism based on transitions between zero-field-split states. We derive the absorption cross section for a magnetic dipole transition and apply it to calculate the loss tangent. For Cr, Fe, and V impurities in sapphire, we find loss tangents at 4.5 GHz in the range of 10⁻⁹–10⁻⁸, again comparable to the loss measured in experiments.

Work performed in collaboration with Mark Turiansky and supported by DOE.

[1] M. E. Turiansky and C. G. Van de Walle, APL Quantum 1, 026114 (2024).